Download Algebraic Topology via Differential Geometry by M. Karoubi, C. Leruste PDF

By M. Karoubi, C. Leruste

During this quantity the authors search to demonstrate how equipment of differential geometry locate program within the learn of the topology of differential manifolds. must haves are few because the authors take pains to set out the speculation of differential varieties and the algebra required. The reader is brought to De Rham cohomology, and particular and targeted calculations are current as examples. subject matters coated contain Mayer-Vietoris specified sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This publication might be compatible for graduate scholars taking classes in algebraic topology and in differential topology. Mathematicians learning relativity and mathematical physics will locate this a useful advent to the suggestions of differential geometry.

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Download Modern Differential Geometry for Physicists by Chris J Isham PDF

By Chris J Isham

This version of the precious textual content smooth Differential Geometry for Physicists comprises an extra bankruptcy that introduces a few of the easy principles of normal topology wanted in differential geometry. a couple of small corrections and additions have additionally been made.

These lecture notes are the content material of an introductory direction on sleek, coordinate-free differential geometry that is taken via first-year theoretical physics PhD scholars, or by means of scholars attending the one-year MSc direction "Fundamental Fields and Forces" at Imperial university. The e-book is worried fullyyt with arithmetic right, even though the emphasis and exact subject matters were selected considering the way differential geometry is utilized nowadays to trendy theoretical physics. This comprises not just the normal region of basic relativity but additionally the speculation of Yang-Mills fields, nonlinear sigma versions and different kinds of nonlinear box platforms that characteristic in sleek quantum box concept.

The quantity is split into 4 elements: (i) creation to normal topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical points of the idea of Lie teams and Lie crew activities on manifolds; (iv) creation to the speculation of fibre bundles. within the creation to differential geometry the writer lays substantial tension at the easy principles of "tangent house structure", which he develops from a number of varied issues of view - a few geometrical, others extra algebraic. this can be performed with know-how of the trouble which physics graduate scholars usually event while being uncovered for the 1st time to the quite summary principles of differential geometry.

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Download Elementary Differential Geometry of Plane Curves by R H. 1889-1944 Fowler PDF

By R H. 1889-1944 Fowler

This specified account of simple differential homes of airplane curves presents a hyperlink among research and extra advanced geometrical theorems, providing historical past and perform to geometry and research scholars.

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Download The geometric topology of 3-manifolds by R. H. Bing PDF

By R. H. Bing

This booklet belongs in either graduate and undergraduate libraries as an invaluable reference for college students and researchers in topology. it really is directed towards mathematicians attracted to geometry who've had no less than a starting direction in topology. it's going to give you the reader with a greater realizing of the actual houses of Euclidean 3-space--the house within which we presume we are living. The reader should still examine of a few unsolved difficulties that proceed to baffle reseachers. the main profound bring about the amount is the facet approximation theorem. in spite of the fact that, a number of the initial effects and a few of the purposes can be utilized extra usually for reference.

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Download Differential Geometry: Manifolds, Curves, and Surfaces by Marcel Berger, Bernard Gostiaux, Silvio Levy PDF

By Marcel Berger, Bernard Gostiaux, Silvio Levy

This e-book comprises components, varied in shape yet comparable in spirit. the 1st, which includes chapters zero via nine, is a revised and a bit enlarged model of the 1972 e-book Geometrie Differentielle. the second one half, chapters 10 and eleven, is an try and therapy the infamous absence within the unique e-book of any remedy of surfaces in three-space, an omission all of the extra unforgivable in that surfaces are one of the most universal geometrical gadgets, not just in arithmetic yet in lots of branches of physics. Geometrie Differentielle was once in response to a path I taught in Paris in 1969- 70 and back in 1970-71. In designing this direction i used to be decisively influ­ enced via a talk with Serge Lang, and that i enable myself be guided by means of 3 basic principles. First, to prevent making the assertion and facts of Stokes' formulation the climax of the path and working out of time ahead of any of its purposes may be mentioned. moment, to demonstrate every one new proposal with non-trivial examples, once attainable after its introduc­ tion. and at last, to familiarize geometry-oriented scholars with research and analysis-oriented scholars with geometry, a minimum of in what matters manifolds.

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Download Manifolds, Tensors, and Forms: An Introduction for by Paul Renteln PDF

By Paul Renteln

Offering a succinct but accomplished remedy of the necessities of contemporary differential geometry and topology, this book's transparent prose and casual type make it obtainable to complex undergraduate and graduate scholars in arithmetic and the actual sciences. The textual content covers the fundamentals of multilinear algebra, differentiation and integration on manifolds, Lie teams and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and measure conception. It additionally good points over 250 distinctive routines, and numerous purposes revealing primary connections to classical mechanics, electromagnetism (including circuit theory), common relativity and gauge concept. strategies to the issues can be found for teachers at www.cambridge.org/9781107042193

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Download Riemannian Geometry by Manfredo P.Do Carmo, M.P. do Carmo, Francis Flaherty PDF

By Manfredo P.Do Carmo, M.P. do Carmo, Francis Flaherty

This article has been followed at:

University of Pennsylvania, Philadelphia college of Connecticut, Storrs Duke collage, Durham, NC California Institute of expertise, Pasadena collage of Washington, Seattle Swarthmore university, Swarthmore, PA college of Chicago, IL collage of Michigan, Ann Arbor

"In the reviewer's opinion, this can be a remarkable e-book which makes studying a true pleasure."

- Revue Romaine de Mathematiques Pures et Appliquees

"This main-stream presentation of differential geometry serves good for a direction on Riemannian geometry, and it really is complemented through many annotated exercises."

- Monatshefte F. Mathematik

"This is without doubt one of the most sensible (if even not only the simplest) ebook should you are looking to get an excellent, soft and quickly, yet but thorough creation to trendy Riemannian geometry."

- Publicationes Mathematicae

Contents: Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * whole Manifolds; Hopf-Rinow and Hadamard Theorems * areas of continuous Curvature * adaptations of power * The Rauch comparability Theorem * The Morse Index Theorem * the elemental staff of Manifolds of damaging Curvature * the sector Theorem * Index

Series: arithmetic: thought and functions

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Download A Panoramic View of Riemannian Geometry by Marcel Berger PDF

By Marcel Berger

This e-book introduces readers to the dwelling themes of Riemannian Geometry and information the most effects identified to this point. the consequences are said with out special proofs however the major rules concerned are defined, affording the reader a sweeping panoramic view of just about the whole thing of the sector.

From the studies ''The publication has intrinsic worth for a pupil in addition to for an skilled geometer. also, it truly is a compendium in Riemannian Geometry.'' --MATHEMATICAL REVIEWS

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Download Geometry and analysis on manifolds : in memory of professor by Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro PDF

By Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, Alan Weinstein

This quantity is devoted to the reminiscence of Shoshichi Kobayashi, and gathers contributions from individual researchers engaged on themes with regards to his study components. The publication is prepared into 3 elements, with the 1st half proposing an summary of Professor Shoshichi Kobayashi’s profession. this can be by way of expository path lectures (the moment half) on contemporary themes in extremal Kähler metrics and price distribution conception, so that it will be precious for graduate scholars in arithmetic drawn to new subject matters in complicated geometry and complicated research. finally, the 3rd a part of the amount collects authoritative learn papers on differential geometry and intricate analysis.

Professor Shoshichi Kobayashi was once a well-known foreign chief within the components of differential and complicated geometry. He contributed an important rules which are nonetheless thought of basic in those fields. The e-book might be of curiosity to researchers within the fields of differential geometry, complicated geometry, and a number of other complicated variables geometry, in addition to to graduate scholars in mathematics.

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Download Geometric Optimal Control: Theory, Methods and Examples by Heinz Schättler, Urszula Ledzewicz (auth.) PDF

By Heinz Schättler, Urszula Ledzewicz (auth.)

This e-book provides a entire remedy of the elemental worthy and adequate stipulations for optimality for finite-dimensional, deterministic, optimum keep an eye on difficulties. The emphasis is at the geometric facets of the speculation and on illustrating how those tools can be utilized to resolve optimum keep watch over difficulties. It offers instruments and methods that move way past common strategies and will be used to procure an entire knowing of the worldwide constitution of suggestions for the underlying challenge. The textual content encompasses a huge quantity and diversity of absolutely labored out examples that diversity from the classical challenge of minimal surfaces of revolution to melanoma therapy for novel treatment ways. these kind of examples, in a single means or the opposite, illustrate the ability of geometric options and strategies. The flexible textual content comprises fabric on assorted degrees starting from the introductory and straight forward to the complicated. components of the textual content should be seen as a accomplished textbook for either complicated undergraduate and all point graduate classes on optimum regulate in either arithmetic and engineering departments. The textual content strikes easily from the extra introductory subject matters to these elements which are in a monograph type have been complicated themes are provided. whereas the presentation is mathematically rigorous, it truly is performed in an academic kind that makes the textual content available to a large viewers of researchers and scholars from quite a few fields, together with the mathematical sciences and engineering. Heinz Schättler is an affiliate Professor at Washington college in St. Louis within the division of electric and structures Engineering, Urszula Ledzewicz is a exotic examine Professor at Southern Illinois college Edwardsville within the division of arithmetic and Statistics.

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